Properties of Bridge Circuits MCQ Quiz in தமிழ் - Objective Question with Answer for Properties of Bridge Circuits - இலவச PDF ஐப் பதிவிறக்கவும்
Last updated on Mar 17, 2025
Latest Properties of Bridge Circuits MCQ Objective Questions
Top Properties of Bridge Circuits MCQ Objective Questions
Properties of Bridge Circuits Question 1:
In the AC bridge, shown in the figure R = 103 Ω and C = 10-7 F. If the bridge is balanced at a frequency ω0, the value of ω0 in rad/s is-
Answer (Detailed Solution Below) 10000
Properties of Bridge Circuits Question 1 Detailed Solution
At balance condition,
Z1 Z4 = Z2 Z3
\(\Rightarrow R\left[ {R + \frac{1}{{j\omega c}}} \right] = 2R\;\left[ {\frac{{R\left( {\frac{1}{{j\omega c}}} \right)}}{{R + \frac{1}{{j\omega c}}}}} \right]\)
\(\Rightarrow R\left[ {R + \frac{1}{{j\omega c}}} \right] = 2R\;\left[ {\frac{R}{{1 + jR\omega c}}} \right]\)
\(\Rightarrow \left[ {R + \frac{1}{{j\omega c}}} \right]\left[ {1 + j\omega RC} \right] = 2R\)
\(\Rightarrow \left( {R + R} \right) + \frac{1}{{j\omega c}} + j\omega {R^2}c = 2R\)
\(\Rightarrow j\omega {R^2}C = \frac{{ - 1}}{{j\omega c}}\)
\(\Rightarrow {\omega ^2}{R^2}{C^2} = 1 \Rightarrow \omega = \frac{1}{{RC}} = \frac{1}{{{{10}^3} \times {{10}^{ - 7}}}} = 10000\;rad/s\)
Properties of Bridge Circuits Question 2:
For the bridge shown Z1 = 200 ∠20° Ω, Z2 = 150 ∠30° Ω and Z3 = 300 ∠-30° Ω. What is the value of Z4 so that the bridge is balanced?
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 2 Detailed Solution
At bridge balance condition,
Z1 Z4 = Z2 Z3
⇒ 200 ∠20° Z4 = 150 ∠30° 300 ∠-30°
⇒ Z4 = 225 ∠-20° ΩProperties of Bridge Circuits Question 3:
The impedance of a basic ac bridge arms are ZAB = 300 Ω, ZBC = 150 Ω ∠60°, ZCD = 400 Ω/30° ZDA = unknown if ω = 1000 radian/s, the components of the unknown arms has the resistance 692.82 in
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 3 Detailed Solution
For bridge balance:
ZAB × ZCD = ZBC × ZAD
300 × 400 ∠30° = ZAD × 150 ∠60°
800 ∠30° = ZAD ∠60°
ZAD = 692.82 – j 400
Capacitive reactance \({x_c} = \frac{1}{{wc}}\)
\(C = \frac{1}{{400 \times 1000}} = 2.5\mu F\)
Properties of Bridge Circuits Question 4:
In the AC bridge shown in figure R = 105 Ω and C = 10-8 F. If the bridge is balanced at a frequency ωo, the value of ω0 in rad/sec is _______.
Answer (Detailed Solution Below) 1000
Properties of Bridge Circuits Question 4 Detailed Solution
\(R \times \left( {R + \frac{1}{{j\omega C}}} \right) = 2R \times \frac{R}{{1 + j\omega RC}}\)
\(\frac{{1 + j\omega RC}}{{j\omega RC}} = \frac{{2R}}{{1 + j\omega RC}}\)
(1 + jωRC)2 = jωR2C
1 + 2jωRC – ω2R2C2 = jωR2C
Equate real part
1 – ω2R2C2 = 0
\({\omega ^2} = \frac{1}{{{R^2}{C^2}}}\)
\(\omega = \frac{1}{{RC}}\)
Now put value of R and C
\(\omega = \frac{1}{{{{10}^6} \times {{10}^{ - 8}}}} = {10^3}rad/sec\)
Properties of Bridge Circuits Question 5:
The a.c. bridge in figure remains balance if z comprises of
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 5 Detailed Solution
At bridge balance condition,
\(\begin{array}{l} ({R_1})\left( {\frac{1}{{j\omega {C_1}}}} \right) = z\left( {\;{R_2} + \frac{1}{{j\omega {C_2}}}} \right)\\ z = \frac{{({R_1})\left( {\frac{1}{{j\omega {C_1}}}} \right)}}{{\left( {\;{R_2} + \frac{1}{{j\omega {C_2}}}} \right)}} \end{array}\)
It is equivalent to a resistor and a capacitor are connected in parallel.Properties of Bridge Circuits Question 6:
Find the excitation frequency (in Hz) in the Ac Bridge shown in figure under balance condition. The circuit component values are given as
R1 = 100 kΩ,
R3 = R4 = 100 kΩ,
C1 = 2 C2 = 10 nF
Answer (Detailed Solution Below) 158 - 160
Properties of Bridge Circuits Question 6 Detailed Solution
under bridge balance condition,
\(\left[ {{R_1} + \frac{1}{{j\omega {c_1}}}} \right]{R_4} = {R_3}\left[ {\frac{{{R_2}\left( {\frac{1}{{j\omega {c_2}}}} \right)}}{{{R_2} + \frac{1}{{j\omega {c_2}}}}}} \right]\)
Given that, \({R_3} = {R_4}\)
\(\left[ {{R_1} + \frac{1}{{j\omega {c_1}}}} \right] = \left[ {\frac{{{R_2}\left( {\frac{1}{{j\omega {c_2}}}} \right)}}{{{R_2} + \frac{1}{{j\omega {c_2}}}}}} \right]\)
\(\left[ {{R_1} + \frac{1}{{j\omega {c_1}}}} \right] = \left[ {\frac{{{R_2}}}{{{R_2}j\omega {c_2} + 1}}} \right]\)
\(\begin{array}{l} \frac{{\left( {{R_{1\;}}j\omega {c_1} + 1} \right)}}{{j\omega {c_1}}} = \frac{{{R_2}}}{{j{R_2}\omega {c_2} + 1}}\\ \left( {1 + \;j\omega {R_1}{C_1}} \right)\left( {1 + \;j\omega {R_2}{C_2}} \right) = j\omega {C_1}{R_2}\\ 1 + \;j\omega {R_1}{C_1} + \;j\omega {R_2}{C_2} - {\omega ^2}{R_1}{R_2}{C_1}{C_2} = \;j\omega {C_1}{R_2} \end{array}\)
By comparing real parts on both sides,
\(\begin{array}{l} 1 - {\omega ^2}{R_1}{R_2}{C_1}{C_2} = 0\\ \omega = \frac{1}{{\sqrt {{R_1}{R_2}{C_1}{C_2}} }} \end{array}\)
By comparing imaginary parts on both sides,
\(\begin{array}{l} {R_1}{C_1} + {R_2}{C_2} = {C_1}{R_2}\\ {R_2} = \left( {{C_1} - {C_2}} \right) = {R_1}{C_1}\\ {R_2} = \frac{{{R_1}{C_1}}}{{\left( {{C_1} - {C_2}} \right)}} = \frac{{100 \times {{10}^3} \times 10 \times {{10}^{ - 9}}}}{{\left( {10 \times {{10}^{ - 9}} - 5 \times {{10}^{ - 9}}} \right)}}\\ = 200\:k\Omega \;\\ f = \frac{1}{{2 \pi \sqrt {{R_1}{R_2}{C_1}{C_2}} }}\\ =\frac{1}{{2\pi \sqrt {100 \times {{10}^3} \times 200 \times {{10}^3} \times 10 \times {{10}^{ - 9}} \times 5 \times {{10}^{ - 9}}} }} \end{array}\)
= 159.15 HzProperties of Bridge Circuits Question 7:
The bridge circuit in figure is balanced. The magnitude of current I is
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 7 Detailed Solution
At bridge balance condition,
\(\begin{array}{l} {V_A} = {V_B}\\ {V_A} = {V_S}\left( {\frac{4}{{1 + 4}}} \right) = \frac{{4{V_S}}}{5}\\ {V_B} = {V_S} - 2\\ \frac{{4{V_S}}}{5} = {V_S} - 2\\ 4{V_S} = 5{V_S} - 10\\ {V_S} = 10V\\ I = \frac{{{V_S}}}{{5 \times {{10}^3}}} + \frac{{{V_S} - 2}}{{2 \times {{10}^3}}}\\ I = \frac{{10}}{{5 \times {{10}^3}}} + \frac{8}{{2 \times {{10}^3}}}\\ I = 6\;mA \end{array}\)
Properties of Bridge Circuits Question 8:
The impedances of a basic ac bridge arms are
ZAB = 250 Ω
ZBC = 100 ∠60° Ω
ZCD = 400 ∠30° Ω
ZDA = Unknown
If ω = 1000 radian/sec, the components of the unknown arm has the resistance 500√3 Ω isAnswer (Detailed Solution Below)
Properties of Bridge Circuits Question 8 Detailed Solution
At bridge balance condition,
\(\frac{{{Z_{AB}}}}{{{Z_{DA}}}} = \frac{{{Z_{BC}}}}{{{Z_{CD}}}}\)
\(\frac{{250}}{{{Z_{DA}}}} = \frac{{100\angle 60}}{{400\angle 30}}\)
\({Z_{DA}} = \frac{{250 \times 400\angle 30}}{{100\angle 60}}\)
\({Z_{DA}} = 1000\angle - 30\)
\(= \left( {1000 \times \frac{{\sqrt 3 }}{2} - j\;500} \right){\rm{\Omega }}\)
\({Z_{DA}} = \left( {500 \times \sqrt 3 - j\;500} \right)\)
Negative sign of reactance value indicates that, it is capacitive reactance.
\({X_c} = 500\)
\(\frac{1}{{\omega C}} = 500\)
\(C = \frac{1}{{\left( {500} \right)\left( {1000} \right)}} = 2 \times {10^{ - 6}}F = 2\mu F\)
Hence ZDA is a resistance of 500√3 Ω in series with a capacitor of 2 μF
Properties of Bridge Circuits Question 9:
If the given circuit is a balanced bridge, what should be in place of ‘X’ ?
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 9 Detailed Solution
For balanced bridge, Z1Z4 = Z2Z3
\(X{R_4} = \left( {{R_2} - \frac{J}{{\omega {C_2}}}} \right){R_3}\)
\(X = \frac{{{R_2}{R_3}}}{{{R_4}}} - J\frac{1}{{\frac{{\omega {C_2}{R_4}}}{{{R_3}}}}}\)
X = resistance and capacitance in series.Properties of Bridge Circuits Question 10:
For the given circuit, if the current through branch BD is zero what is the value of battery current I in mA upto two decimal places?
Answer (Detailed Solution Below) 42.8 - 43.0
Properties of Bridge Circuits Question 10 Detailed Solution
If current through BD is zero, then the bridge is balanced.
For balanced bridge, R × 75 = 150 × 100
R = 200 Ω
Equivalent resistance of the circuit, Req = 350 || 175
= 116.67 Ω
\(I = \frac{5}{{116.67}} = 0.04286A = 42.86mA\)